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Formative instructional & assessment tasks for the common core state standards in mathematics

Formative instructional & assessment tasks for the common core state standards in mathematics

GRADE
2
PUBLIC SCHOOLS OF NORTH CAROLINA
State Board of Education | Department of Public Instruction
Formative Instructional & Assessment Tasks
for the Common Core State Standards in Mathematics
Word Document versions of the documents
http://commoncoretasks.wikispaces.com/
STATE BOARD OF EDUCATION
The guiding mission of the North Carolina State Board of Education is that every public school student will graduate
from high school, globally competitive for work and postsecondary education and prepared for life in the 21st Century.
NC DEPARTMENT OF PUBLIC INSTRUCTION
June St. Clair Atkinson, Ed.D., State Superintendent
301 N. Wilmington Street :: Raleigh, North Carolina 27601-2825
In compliance with federal law, NC Public Schools administers all state-operated educational programs, employment activities and
admissions without discrimination because of race, religion, national or ethnic origin, color, age, military service, disability, or gender,
except where exemption is appropriate and allowed by law.
Inquiries or complaints regarding discrimination issues should be directed to:
Dr. Rebecca Garland, Chief Academic Officer :: Academic Services and Instructional Support
6368 Mail Service Center, Raleigh, NC 27699-6368 :: Telephone: (919) 807-3200 :: Fax: (919) 807-4065
Visit us on the Web :: www.ncpublicschools.org
WILLIAM C. HARRISON
Chairman :: Fayetteville
WAYNE MCDEVITT
Vice Chair :: Asheville
WALTER DALTON
Lieutenant Governor :: Rutherfordton
JANET COWELL
State Treasurer :: Raleigh
Jean W. Wolard
Plymouth
REGINALD KENAN
Rose Hill
KEVIN D. HOWELL
Raleigh
SHIRLEY E. HARRIS
Troy
CHRISTINE J. GREENE
High Point
JOHN A. TATE III
Charlotte
ROBERT “TOM” SPEED
Boone
MELISSA E. BARTLETT
Roxboro
PATRICIA N. WILLOUGHBY
Raleigh
M0910
Table
of
Contents
1. Common
Core
State
Standards
........................................................................................................................................
1
2. Administration
Manual
.......................................................................................................................................................
3
3. Operations
&
Algebraic
Thinking
................................................................................................................................
15
4. Number
and
Operations
in
Base
Ten
........................................................................................................................
126
5. Measurement
and
Data
..................................................................................................................................................
158
6. Geometry
..............................................................................................................................................................................
203
7. Student
Record
Keeping
Forms
.................................................................................................................................
221
NOTE:
The
separate
Word
document
versions
of
each
section
can
be
found
online
at
http://commoncoretasks.wikispaces.com/
.
Common Core
State Standards
Operations and Algebraic Thinking
Represent and solve problems involving addition and subtraction.
2.OA.1 Use addition and subtraction within 100 to solve one- and two-step
word problems involving situations of adding to, taking from, putting
together, taking apart, and comparing, with unknowns in all positions,
e.g., by using drawings and equations with a symbol for the unknown
number to represent the problem. (Note: See Glossary, Table 1.)
Add and subtract within 20.
2.OA.2 Fluently add and subtract within 20 using mental strategies. (Note:
See standard 1.OA.6 for a list of mental strategies). By end of
Grade 2, know from memory all sums of two one-digit numbers.
Work with equal groups of objects to gain foundations for multiplication.
2.OA.3 Determine whether a group of objects (up to 20) has an odd or even
number of members, e.g., by pairing objects or counting them by 2s; write
an equation to express an even number as a sum of two equal addends.
2.OA.4 Use addition to find the total number of objects arranged in
rectangular arrays with up to 5 rows and up to 5 columns; write an
equation to express the total as a sum of equal addends.
Number and Operations in Base Ten
Understand place value.
2.NBT.1 Understand that the three digits of a three-digit number represent
amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0
tens, and 6 ones. Understand the following as special cases:
a. 100 can be thought of as a bundle of ten tens – called a “hundred.”
b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one,
two, three, four, five, six, seven, eight, or nine hundreds
(and 0 tens and 0 ones).
2.NBT.2 Count within 1000; skip-count by 5s, 10s, and 100s.
2.NBT.3 Read and write numbers to 1000 using base-ten numerals, number
names, and expanded form.
2.NBT.4 Compare two three-digit numbers based on meanings of the
hundreds, tens, and ones digits, using >, =, and < symbols to record
the results of comparisons.
Use place value understanding and properties of operations to add and
subtract.
2.NBT.5 Fluently add and subtract within 100 using strategies based on
place value, properties of operations, and/or the relationship
between addition and subtraction.
2.NBT.6 Add up to four two-digit numbers using strategies based on place
value and properties of operations.
2.NBT.7 Add and subtract within 1000, using concrete models or drawings
and strategies based on place value, properties of operations,
and/or the relationship between addition and subtraction; relate
the strategy to a written method. Understand that in adding or
subtracting three-digit numbers, one adds or subtracts hundreds
and hundreds, tens and tens, ones and ones; and sometimes it is
necessary to compose or decompose tens or hundreds.
2.NBT.8 Mentally add 10 or 100 to a given number 100-900, and mentally
subtract 10 or 100 from a given number 100-900.
2.NBT.9 Explain why addition and subtraction strategies work, using place
value and the properties of operations. (Note: Explanations may be
supported by drawings or objects.)
Measurement and Data
Measure and estimate lengths in standard units.
2.MD.1 Measure the length of an object by selecting and using appropriate
tools such as rulers, yardsticks, meter sticks, and measuring tapes.
2.MD.2 Measure the length of an object twice, using length units of
different lengths for the two measurements; describe how the two
measurements relate to the size of the unit chosen.
2.MD.3 Estimate lengths using units of inches, feet, centimeters, and meters.
2.MD.4 Measure to determine how much longer one object is than another,
expressing the length difference in terms of a standard length unit.
Relate addition and subtraction to length.
2.MD.5 Use addition and subtraction within 100 to solve word problems
involving lengths that are given in the same units, e.g., by using
drawings (such as drawings of rulers) and equations with a symbol
for the unknown number to represent the problem.
2.MD.6 Represent whole numbers as lengths from 0 on a number line
diagram with equally spaced points corresponding to the numbers
0, 1, 2, ..., and represent whole-number sums and differences within
100 on a number line diagram.
Second Grade – Standards
1. Extending understanding of base-ten notation – Students extend their
understanding of the base-ten system. This includes ideas of counting
in fives, tens, and multiples of hundreds, tens, and ones, as well as
number relationships involving these units, including comparing. Students
understand multi-digit numbers (up to 1000) written in base-ten notation,
recognizing that the digits in each place represent amounts of thousands,
hundreds, tens, or ones (e.g., 853 is 8 hundreds + 5 tens + 3 ones).
2. Building fluency with addition and subtraction – Students use
their understanding of addition to develop fluency with addition and
subtraction within 100. They solve problems within 1000 by applying their
understanding of models for addition and subtraction, and they develop,
discuss, and use efficient, accurate, and generalizable methods to
compute sums and differences of whole numbers in base-ten notation,
using their understanding of place value and the properties of operations.
They select and accurately apply methods that are appropriate for
the context and the numbers involved to mentally calculate sums and
differences for numbers with only tens or only hundreds.
3. Using standard units of measure – Students recognize the need for
standard units of measure (centimeter and inch) and they use rulers and
other measurement tools with the understanding that linear measure
involves iteration of units. They recognize that the smaller the unit, the
more iterations they need to cover a given length.
4. Describing and analyzing shapes – Students describe and analyze
shapes by examining their sides and angles. Students investigate,
describe, and reason about decomposing and combining shapes to make
other shapes. Through building, drawing, and analyzing two- and three-dimensional
shapes, students develop a foundation for understanding
attributes of two- and three-dimensional shapes, students develop a
foundation for understanding area, volume, congruence, similarity, and
symmetry in later grades.
Mathematical Practices
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
1
Work with time and money.
2.MD.7 Tell and write time from analog and digital clocks to the nearest five
minutes, using a.m. and p.m.
2.MD.8 Solve word problems involving dollar bills, quarters, dimes, nickels,
and pennies, using $ and ¢ symbols appropriately. Example: If you
have 2 dimes and 3 pennies, how many cents do you have?
Represent and interpret data.
2.MD.9 Generate measurement data by measuring lengths of several
objects to the nearest whole unit, or by making repeated
measurements of the same object. Show the measurements by
making a line plot, where the horizontal scale is marked off in whole-number
units.
2.MD.10 Draw a picture graph and a bar graph (with single-unit scale) to
represent a data set with up to four categories. Solve simple put
together, take-apart, and compare problems using information
presented in a bar graph. (Note: See Glossary, Table 1.)
Geometry
Reason with shapes and their attributes.
2.G.1 Recognize and draw shapes having specified attributes, such as
a given number of angles or a given number of equal faces. (Note:
Sizes are compared directly or visually, not compared by measuring.)
Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
2.G.2 Partition a rectangle into rows and columns of same-size squares and
count to find the total number of them.
2.G.3 Partition circles and rectangles into two, three, or four equal shares,
describe the shares using the words halves, thirds, half of, a third of,
etc., and describe the whole as two halves, three thirds, four fourths.
Recognize that equal shares of identical wholes need not have the
same shape.
2
Administration
Manual
K-2 Assessment in North Carolina
In response to North Carolina legislative and State Board requirements, the NC Department of
Public Instruction provides Local Education Agencies with state-developed assessments to be
implemented for Kindergarten, First and Second Grades. These assessments are to include
documented, on-going individualized assessments throughout the year and a summative
evaluation at the end of the year. These assessments monitor proficiency of the standards in the
North Carolina Standard Course of Study: Common Core State Standards for Mathematics.
Assessments may take the form of these state developed materials, adaptations of these
materials, or unique assessments adopted by local school boards. The intended purposes of these
assessments are:
• To provide information about progress of each student for instructional adaptations and early
interventions.
• To provide next-year teachers with information about the status of each of their incoming
students.
• To inform parents about the status of their children relative to grade-level standards at the
end of the year
• To provide the school and school district information about the achievement status and
progress of groups of students in grades K, 1, and 2.
The North Carolina Department of Public Instruction is committed to continued development of
quality teaching and on-going classroom assessment as essential preparation for the students to
master rigorous standards as defined by the NC Standard Course of Study: Common Core State
Standards and Essential Standards. We believe the strategies that engage students in self-assessment,
greater ownership of their learning, communicating, reasoning, problem posing and
problem solving result in long-term growth and learning.
Therefore, the Formative Instructional and Assessment Tasks for Mathematics are designed to
clarify the bond that links quality assessment and effective teaching- and subsequently effective
schools. Learning takes place one student at a time, and quality teaching and assessment is
essential in ensuring that every public school student will graduate from high school, globally
competitive for work and postsecondary education and prepared for life in the 21st Century.
These state-developed assessment materials are aligned with the Common Core State
Standards for Mathematics and may be adopted or modified as appropriate for individual
school districts. As you use them with students, add to and adapt the materials in order to
make them useful for each school’s unique situation. The North Carolina Department of
Public Instruction appreciates any suggestions and feedback, which will help improve upon
this resource. Feedback may be sent to NCDPI Elementary Mathematics Consultant Amy
Scrinzi (Amy.Scrinzi@dpi.nc.gov).
3
K-2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION
The Purpose of the Formative Instructional and Assessment Tasks
The Formative Instructional and Assessment Tasks are provided as tools to use to assess
Kindergarten, First Grade and Second Grade students’ mathematical understanding as specified
in the NC Standard Course of Study: Common Core State Standards for Mathematics (CCSS-M).
Mathematical Concepts Assessed
The Formative Instructional and Assessment Tasks are designed to reveal the extent to which a
student knows and understands specific concepts. Moving beyond only whether an answer is
right or wrong, the tasks focus attention on the thinking and processes that all students use in
solving the tasks, with opportunities to demonstrate his or her knowledge, skill, and
understanding.
Therefore, the tasks assess the Common Core State Standards and highlight Standards for
Mathematical Practice that may emerge as students explore the tasks. The Continuum for
Understanding specifically addresses the conceptual understandings indicated in the CCSS-M.
The Standards for Mathematical Practice that are likely to emerge are indicated in bold for
each task.
Types of Tasks
When assessing young children, it is important to remember that
they frequently know more than they can record in traditional,
symbolic formats. “Age, fluency with language, and experiences
influence how successful students are likely to write a strong
explanation or offer an explanation orally” (Joyner & Muri, 2011).
Therefore interviews, as well as written responses, are provided.
Interview: The teacher asks a series of questions to one
student and carefully listens to the student’s responses
and observes the student’s strategies and thinking as the
student works.
Written Response: The teacher presents a problem to one or more students and asks the
students to use pictures, numbers, and words to show their thinking and explain their reasoning.
Since both correct answers and appropriate processes are valued in mathematics, teachers find that
observing students and talking with them are ways to provide students with opportunities to
demonstrate what they know and can apply in new situations. Thus, the teacher is encouraged to ask
the student clarifying questions during the assessment or after the assessment to gain a more
accurate picture of what the student knows and understands. Insight into children’s thinking helps
teachers build on what students understand, not just what they can do by memorizing processes.
“Without the
conversations or
written explanations,
we have no clue as
to the students’
logic behind their
wrong answers.”
(Joyner & Muri, 2011, p. 250)
4
K-2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION
The Role of the Classroom Teacher
The classroom teacher uses the tasks in a formative manner. As defined by North Carolina
Department of Public Instruction, formative assessment is a
process
used
by
teachers
and
students
during
instruction
that
provides
feedback
to
adjust
ongoing
teaching
and
learning
to
help
students
improve
their
achievement
of
intended
instructional
outcomes. Therefore,
a teacher may use these tasks to:
• Determine prior knowledge regarding a concept that is about to be taught.
• Assess understanding throughout an instructional sequence to gain an understanding
of how to best meet the needs of all of the students in an on-going basis.
• Determine if the student is Developing Understanding of a particular concept or if the
student has Complete Understanding, demonstrating proficiency.
• Assess understanding after the instructional sequence to determine if all students are
proficient with that concept and are ready to move forward.
The teacher may administer the tasks to a whole class, small group of children, or an individual
student, depending on the purpose for collecting data. For example, the teacher may decide that
s/he would like to gain awareness of the entire class’ understanding of a particular concept.
Thus, the task(s) selected would then be administered to all of the students in the class. Other
times the teacher may need to determine what a particular student, or small group of students,
understands in order to plan the most effective mathematical experiences. Thus, the task(s)
selected would then be used with the selected student(s). Therefore, the assessment tasks can be
used in multiple ways with the purpose of informing instructional planning and practice.
The Role of the Local Education Agency (LEA)
A school district may decide to use the assessment tasks to create benchmark assessments,
aligning a collection of tasks to their unique pacing guide to be administered district-wide at
several points throughout the year. The classroom teacher scores the quarterly benchmark
assessments, sees students’ answers, observes misconceptions, and uses the data gathered to
inform further instruction and plan interventions or enrichments as needed (Joyner & Muri,
2011). The district uses the data from the benchmark assessments to gain a global view of how
students are performing within particular domains or clusters, determine which additional
instructional materials and resources may be needed, and discern particular topics and concepts
that teachers may need additional support or growth and work with principals and teachers to
plan professional development and coaching opportunities accordingly.
These state-developed assessment tasks are aligned with the North Carolina Standard
Course of Study: Common Core State Standards for Mathematics and may be adopted or
modified as appropriate for individual school districts. As they are used with students,
please add to and adapt the materials in order to make them useful for each school’s
unique situation. The North Carolina Department of Public Instruction appreciates any
suggestions and feedback, which will help improve upon this resource.
5
K-2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION
The Components of the Formative Instructional & Assessment Tasks
The Formative Instructional and Assessment Tasks are composed of four parts:
1. Assessment Tasks
2. Student Forms
3. Blackline Masters
4. Class/Student Summaries
1. Assessment Tasks
The assessment tasks inform the classroom teacher of a) the Mathematical Concepts addressed,
b) the materials needed, c) the assessment task directions, the d) Continuum of Understanding,
and the e) Standards for Mathematical Practice.
a.) Mathematical Concepts: Designate the domain, cluster, and standard assessed. There may
be some tasks that assess multiple concepts.
Domain: Large group of related standards. Include: Counting and Cardinality (K),
Operations and Algebraic Thinking, Number and Operations in Base Ten, Measurement
and Data, and Geometry.
Cluster: Groups of related standards.
Standard: Define what students should understand and be able to do.
b.) Materials: Student and teacher materials needed to complete the task. Materials may
include: Blackline Master (BLM), Student Form (SF) or classroom materials. Provide additional
materials or substitute materials with those that students use during regular mathematics lessons
as needed.
c.) Task: Directions for the administering the task. May include “Teacher Talk”: dialogue for
the teacher to say to the student(s) while administering the task. Indicated in italics.
d.) Continuum of Understanding: Designates indicators: specific behaviors and skills that
signify if the student is Developing Understanding or demonstrates Complete Understanding.
Indicators: Specific behavior or skill within the continuum noted by a bullet.
Developing Understanding: If the student exhibits one OR more of the indicators listed,
then the student’s understanding is still evolving.
Complete Understanding: If the student exhibits ALL of the indicators listed, then the
student has demonstrated proficiency with that particular skills or concept on that one
particular task. Other tasks may be needed in order to confirm proficiency in that overall
skill or concept.
6
K-2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION
In addition, there may be specific behaviors, strategies, concepts, or skills for which the teacher
is to observe. These are located to the right of the indicators. Answers to the tasks are also
provided in this area.
e.) Standards for Mathematical Practice: Describe processes and dispositions that
mathematically proficient students exhibit. Practices that are likely to emerge as a result of
completing the task are noted in BOLD. The teacher is encouraged to note which practices were
observed during the tasks as well as during daily instruction to gain a global picture of the
mathematical processes and dispositions that the student exhibits.
7
K-2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION
The Formative Instructional and Assessment Tasks are composed of three additional parts:
1. Assessment Tasks
2. Student Forms
3. Blackline Masters
4. Class/Student Summaries
2. Student Forms
Student forms are provided as an option to use for all tasks that require a written response from
the student. These forms are located with the appropriate task and are designated as “SF”.
Teachers may copy, edit, or revise the forms as needed.
3. Blackline Masters
If a task requires a particular illustration or specific materials, then a blackline master is
included. These forms are located with the appropriate task and are designated as “BLM”.
Teachers may copy, edit, or revise forms as needed.
4. Class/Student Summaries
Class and Student Summaries are provided to help the classroom teacher collect and organize
data. These forms are located with the appropriate Domain/Cluster. These forms are provided as
Word documents allowing the teacher to type information as desired, change the size of the
space provided, or add additional columns or categories as needed. Teachers may copy, edit, or
revise the forms as needed.
8
K-2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION
Selecting an Assessment Task
The Formative Instructional and Assessment Tasks are placed with the corresponding
Domain(s), Cluster(s), and Standard(s) on the common core assessment wiki. When searching
for a task, simply click on the domain and cluster of interest. Tasks will be located with each
standard assessed. In addition, each grade is provided with a comprehensive list of assessment
tasks and the standards to which they align.
NOTE: Some tasks assess multiple standards. Therefore, tasks are placed with the
primary standard assessed and additional standards assessed are noted in the table and
with the task directions.
When selecting a task, consider the following:
1. Designate a learning target. What skill or concept do you want students to know?
2. Identify the student(s). Are you curious about all of the students, a handful of students,
or one student in particular? Thinking about the student(s), what are you most interested
in learning that is related to the learning target?
3. Review and select the tasks. Locate tasks that are aligned with the learning target and
address your questions about the student(s).
4. Read the tasks carefully. Which tasks would best uncover student understanding for the
particular learning target? Does it need to be a new task or one previously administered?
Depending on the task and the learning target, the same task could be administered
multiple times over the course of the year.
5. Decide on an amount of tasks. To gain a more accurate view of student knowledge, one
task may not be enough. Perhaps one task, along with classroom evidence, will provide
an appropriate picture of the student’s understanding. Perhaps more than one task is
needed.
6. Decide how the tasks and materials will be presented. Will all students be assessed on
a task at the same time? If so, what will students who finish earlier/later than others do as
other students work? Will students move from one station to another? If so, what will
they do if they have questions about the task? Will students need access to optional
materials? If so, how will they be provided?
“Knowing what is to be learned is the starting point for instructional
planning. This knowledge is also the starting point for determining
what is to be assessed and how it will be measured.”
(Joyner & Muri, 2011, p. 55)
9
K-2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION
Assessing Students
During classroom instruction, the teacher facilitates learning by providing rich tasks, asking
probing questions, observing students, and scaffolding learning as appropriate. However, during
classroom assessment, the classroom teacher wants to learn what a student knows and is able to
do without the support typically provided during instruction.
In order to help the classroom teacher gather the best information possible from the tasks, the
teacher’s role becomes that of an observer. Refraining from any coaching, prompting, or
targeted questioning, the teacher only reads the assessment task to the student as many times as
needed and encourages the student to solve the problem to the best of his/her ability. On
occasion, a word provided in the directions may not make sense to the student and an alternative
word is provided as determined by the teacher. However, the classroom teacher is very careful
not to provide additional information that could cover up what the student does or doesn’t
understand. The goal of assessment is to un-cover student thinking so that instruction can
best meet his/her needs.
As the classroom teacher carefully observes students at work, s/he is finding out as much as
possible about what students are thinking and how they go about working on tasks. The teacher
may take notes on student strategies and behaviors, ask clarifying questions, or restate the
problem as needed. For example, do students work with confidence on the task or are there some
aspects that seem more difficult? Which ones? Can you determine why and make notes for
adjustments next time this happens? Oftentimes, the observation provides the most information
about student thinking.
Because young children frequently know more than they can record in traditional, symbolic
formats, it is important for the teacher to gather as much information about student
understanding as students work on the various tasks. As the teacher circulates, s/he asks
additional questions to learn as much as possible about students’ thinking. For example, the
teacher might say, “Tell me more about the picture you have drawn.” or “Tell me what you are
doing with the counters.” or “Tell me more about your thinking.” The teacher makes notes about
students’ responses.
Consider using the following clarifying questions to help understand student thinking:
• Tell me more about that.
• Can you show me?
• Why do you say that?
• What else can you tell me?
• How do you know?
• Why do you think that happened?
• Do you think this will happen every time?
10
K-2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION
The assessment tasks can be administered individually, in small groups, or as a whole class,
depending on the purpose for the assessment task. Oftentimes, if a task is presented in a whole
class setting, the task requires the student to provide a written response. In this situation, the
teacher is unable to observe all children carefully to learn about their thinking. Therefore, if the
teacher has questions about a student’s work, the teacher is encouraged to ask follow up
questions, clarifying what the student wrote and gaining better insight into the student’s thinking.
When administering a task, consider the following:
1. Prepare the materials. Gather the materials needed for the task. All Blackline masters
and Student Forms are located next to the task. Additional materials from the general
classroom supplies may be needed. Will you need enough for the entire class or just one
or a few students?
2. Read through the task directions. The language that the teacher is to use when
administering a task is provided in italics. This ‘teacher talk’ is provided to help the
classroom teacher ask questions and provide information without guiding thinking.
Comments and notes to the teacher are not in italics. These comments provide prompts
or reminders to the teacher as the task is administered.
3. Read the Continuum for Understanding indicators. Much of the administration of an
assessment task is spent carefully observing children as they work. Read over the
indicators to know what you are looking for as the students solve the problem.
4. Observe the students carefully. How are the students solving the problem? What are
they using? Are they counting everything over and over or are they counting on? Do
they know 10 more or 10 less fluently, or are they counting up or back to figure it out?
Keep a clipboard, tablet, or other documentation devices to take notes as students work.
Oftentimes, the observation provides the most information about student thinking.
5. What’s Next? After a student has completed a task, will s/he head back to Math
Stations? Move on to the next item on his/her contract? Get his/her snack and join the
others on the carpet or on the playground? Use the limited time you have wisely and
refrain from having students wait for one another by planning “what’s next”.
11
K-2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION
Interpreting Data and Making Inferences
The primary purpose of an assessment is to discern student understanding and then use this
knowledge to plan instruction and teach students according to their needs. Because the tasks that
are provided are considered assessments rather than evaluations, proficiency scores are not
provided. Thus, an item is not simply marked as “correct” or “incorrect” or “proficient” or “not
proficient”. Instead, the Continuum of Understanding is provided to help inform the teacher
about the depth to which the student demonstrates understanding.
As student responses are reviewed, the teacher uses the Continuum of Understanding to
determine which strategies, skills, and understanding the student exhibits. Pay particular
attention to what the student DOES understand and what the student does NOT. Both are
equally important in determining the next instructional steps.
The overall goal is that by the end of the year, all students will have become proficient with the
mathematics described for their grade level. Proficient means that they can model and explain
the concepts, they can use the mathematics appropriately and accurately, and they are fluent and
comfortable in applying mathematics.
Giving meaning to students’ words and actions is
not a simple task, but it is critical that the
interpretations are as accurate as possible. Because
decisions about students and teaching arise from
the interpretations, teachers must think carefully
about the mathematics they are teaching, the
continuum of understandings and skills related to
the learning targets, and the information they have
learned from the assessment.
When interpreting data and making inferences, consider the following:
1. Ask Questions: If a student response is unclear or additional questions are needed to
gain clarification about student thinking, have a discussion with the student. Share the
work with the student and ask questions that will uncover the student’s thinking.
Remember, this is not a time to teach the student something s/he may have answered
incorrectly. This is a time to better understand the student’s thinking so that future
instruction can meet his/her needs.
2. Types of Mistakes: Look beyond whether an item’s answer was correct or incorrect by
looking carefully at the types of mistakes that were made. Some mistakes that children
make come from a lack of information. At other times mistakes reflect a lack of
understanding. Remember that there is logic behind students’ answers. The teacher must
look for the reasons for the responses, dig deep and identify any misconceptions that may
exist. Ask questions or seek clarification if needed. “Without the conversations or
written explanations, we have no clue as to the students’ logic behind their wrong
answers.” (Joyner & Muri, 2011, p. 250)
“Unless we take the time to
analyze incorrect responses,
we may have no clue as to why
students miss questions.”
(Joyner & Muri, 2011, p. 123)
12
K-2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION
3. Note Strategies Used: The Continuum of Understanding provides strategies of
particular interest as well as additional skills and knowledge that the student may exhibit.
Carefully note how the student solves the problem present in the task. What strategies
does the student use? Does the student continually use a counting strategy rather than
moving forward to making tens? Are there strategies that are never used? What
strategies need to be highlighted during future instruction?
4. Organize Data: How will you capture the notes made about the student work? Will data
be recorded by individual student, on class summary sheets, or both? Some teachers may
wish to make notes on the task direction sheet for each student and staple it to the student
work. Other teachers may want to use the individual student recording form provided to
capture notes, using the task direction sheet to guide the structure of the notes. Teachers
may also want to compile class data on the class summary sheets to gain a global
perspective of the class as a whole, determine small groups, and determine next
instructional steps.
Assigning meaning to students’ words, actions, and products is perhaps the most difficult part of
assessment. However, teachers must deal with students’ misconceptions as well as their
strengths if students are going to be successful. If decisions are made from too little evidence or
misleading evidence teachers may not plan the necessary classroom experiences for the students
to refine their thinking.
Therefore, it is important to note that these assessment tasks will provide only a part of the
evidence of students’ knowledge and understanding and will be combined with other information
the teacher has gathered about the student. These assessments are not intended to provide a
complete picture of a student’s mathematics understandings. These assessments and additional
student products and anecdotal information will need to be combined to gain the most accurate
picture of student’s ability and understanding of mathematics.
References:
Joyner, J. & Muri, M. (2011). INFORMative assessment: Formative assessment to improve math achievement. Sausalito, CA: Math Solutions.
“When we do not have an opportunity to see the steps or
procedures that students use in determining answers or if students
do not explain their thinking, the correct answers may be the
results or informed guesses rather than solid understanding.”
(Joyner & Muri, 2011, p. 122)
13
K-2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION
A Special Thank-You
The development of the NC Department of Public Instruction K-2 Formative Instructional and
Assessment Tasks was a collaborative effort with a diverse group of dynamic teachers, coaches,
administrators, university faculty, and NCDPI staff. We are very appreciative of all of the time,
support, ideas, and suggestions made in an effort to provide North Carolina with quality
formative assessment items for Kindergarten, First, and Second Grade. The North Carolina
Department of Public Instruction appreciates any suggestions and feedback, which will help
improve upon this resource. Please send all correspondence to Barbara Bissell
(barbara.bissell@dpi.nc.gov) and Amy Scrinzi (amy.scrinzi@dpi.nc.gov).
K-2 Assessment Committee
The K-2 Assessment Committee led the work of the K-2 Assessments. With support of their
school and district, they volunteered their time and effort to develop the K-2 Formative
Instructional and Assessment Tasks.
Jill Burke, First Grade Teacher, Chapel Hill-Carrboro City Schools
Leanne Daughtry, District Office, Johnston County Schools
Andi Greene, First Grade Teacher, Edgecombe County Schools
Tery Gunter, Second Grade Teacher, Durham County Schools
Tesha Isler, Teaching/Learning Coach, Wayne County Schools
Patty Jordan, Second Grade Teacher, Wake County Schools
Rebecca Kidd, Kindergarten Teacher, Asheboro City Schools
Loryn Morrison, District Lead Teacher, Davidson County Schools
Becky Pearce, Kindergarten Teacher, Guilford County Schools
Kitty Rutherford, NCDPI Elementary Consultant
Amy Scrinzi, NCDPI Elementary Consultant
District Support
In a true collaborative effort, districts in North Carolina that had begun implementing the Common
Core State Standards during the 2011-2012 school year voluntarily shared their assessment efforts
with the K-2 Assessment Committee. Many of the final tasks presented are a direct result of this
collaborative support.
Cabarrus, Charlotte-Mecklenburg, Cleveland, Currituck, Davidson, Iredell-Statesville,
Kannapolis, and Union
Critical Friends
Our Critical Friends carefully reviewed the assessment tasks, offered specific feedback, and
provided suggestions for additional tasks as needed. Their feedback guided the final development
of the assessment tasks.
Melanie Burgess, Jeanette Cox, Donna Dalke, Ana Floyd, Sharon Frost, Royanna Jackson,
Jeane Joyner, Rendy King, Carol Midgett, Drew Polly, Wendy Rich, Karen Young, and
Pam Zelando
14
Operations &
Algebraic Thinking
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 1a
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and comparing,
with unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Add To-Start Unknown, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Daniel had some stickers.
His brother gave him 5 more stickers. Now Daniel has 18 stickers. How many stickers did
Daniel have to start with? Write an equation that represents this problem. Use a symbol for
the unknown number.
Solve the problem and use words, numbers or pictures to explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 13 stickers
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 18 - 5 = *; * + 5 = 18).
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
15
OA Task 1a Name ____________________________________
2.OA.1 Add To-Start Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Daniel had some stickers. His brother gave him 5 more stickers. Now Daniel
has 18 stickers. How many stickers did Daniel have to start with?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ stickers
16
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 1b
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and comparing,
with unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Add To-Start Unknown, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Jayden has some baseball
cards. His friend gave him 28 more baseball cards. Now Jayden has 95 baseball cards. How
many baseball cards did John start with? Write an equation that represents this problem.
Use a symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 67 baseball cards
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts
• Equation is accurate (e.g., 95 – 28 = *; 28 + * = 95).
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
17
OA Task 1b Name ____________________________________
2.OA.1 Add To-Start Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Jayden has some baseball cards. His friend gave him 28 more baseball cards.
Now Jayden has 95 baseball cards. How many baseball cards did Jayden start
with?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ baseball cards
18
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 1c
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and
comparing, with unknowns in all positions, e.g., by using drawings and equations with a
symbol for the unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Add To-Start Unknown, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Alice has some pennies.
Her dad gave her 48 more pennies. Now Alice has 83 pennies. How many pennies did Alice
start with? Write an equation that represents this problem. Use a symbol for the unknown
number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 35 pennies
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., * + 48 = 83; 83 – 48 = *).
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
19
OA Task 1c Name ____________________________________
2.OA.1 Add To-Start Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Alice has some pennies. Her dad gave her 48 more pennies. Now Alice has 83
pennies. How many pennies did Alice start with?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ pennies
20
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 1d
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and comparing,
with unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Add To-Start Unknown, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Nevaeh had some jewels.
She gave 11 jewels to her sister. Now Nevaeh has 79 jewels. How many jewels did Nevaeh
have to start with? Write an equation that represents this problem. Use a symbol for the
unknown number.
Solve the problem and use words, numbers or pictures to explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 90 jewels
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 48 - 11 = *; * + 11 = 48).
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
21
OA Task 1d Name ____________________________________
2.OA.1 Add To-Start Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Nevaeh had some jewels. She gave 11 jewels to her sister. Now Nevaeh has 79
jewels. How many jewels did Nevaeh have to start with?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ jewels
22
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 2a
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and comparing,
with unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Take From-Start Unknown, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Some baseball cards were
on the table. Sam took 42 baseball cards. Then there were 26 baseball cards on the table.
How many baseball cards were on the table before? Write an equation that represents this
problem. Use a symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 68 baseball cards
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., * - 42 = 26; 26 + 42 = *).
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
23
OA Task 2a Name ____________________________________
2.OA.1 Take From-Start Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Some baseball cards were on the table. Sam took 42 baseball cards. Then there
were 26 baseball cards on the table. How many baseball cards were on the
table before?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ baseball cards
24
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 2b
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and
comparing, with unknowns in all positions, e.g., by using drawings and equations with a
symbol for the unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Take From-Start Unknown, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Some players are on the
basketball court. 14 players left. Then there were 16 players on the basketball court. How
many players were on the basketball court before? Write an equation that represents this
problem. Use a symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 30 players
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., * - 14 = 16; 14 + 16 = *).
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
25
OA Task 2b Name ____________________________________
2.OA.1 Take From-Start Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Some players are on the basketball court. 14 players left. Then there were 16
players on the basketball court. How many players were on the basketball
court before?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ players
26
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 2c
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and
comparing, with unknowns in all positions, e.g., by using drawings and equations with a
symbol for the unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Take From-Start Unknown, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Some fish are swimming
in the stream. 23 fish swam away. Then there were 31 fish swimming in the stream. How
many fish were swimming in the stream before? Write an equation that represents this
problem. Use a symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 54 fish
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g. 23 + 31 = *).
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
27
OA Task 2c Name ____________________________________
2.OA.1 Take From-Start Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Some fish are swimming in the stream. 23 fish swam away. Then there were 31 fish
swimming in the stream. How many fish were swimming in the stream before?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ fish
28
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 2d
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and
comparing, with unknowns in all positions, e.g., by using drawings and equations with a
symbol for the unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Take From-Start Unknown, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: There were some Legos in
a bucket. 50 Legos spilled out of the bucket. Then there were 33 Legos in the bucket. How
many Legos were in the bucket before? Write an equation that represents this problem. Use
a symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 83 Legos
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 50 + 33 = *; * - 50 = 33).
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
29
OA Task 2d Name ____________________________________
2.OA.1 Take From-Start Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
There were some Legos in a bucket. 50 Legos spilled out of the bucket. Then
there were 33 Legos in the bucket. How many Legos were in the bucket
before?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ Legos
30
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 3a
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and comparing,
with unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Compare- Smaller Unknown: More, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Daniella has 9 more
bracelets than Katie. Katie has 22 bracelets. How many bracelets does Daniella have?
Write an equation that represents this problem. Use a symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 31 bracelets
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 9 + 22 = *).
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
31
OA Task 3a Name ____________________________________
2.OA.1 , 2.NBT.5, 2.NBT.9
Compare- Smaller Unknown: More, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Daniella has 9 more bracelets than Katie. Katie has 22 bracelets. How many
bracelets does Daniella have?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ bracelets
32
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 3b
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and comparing,
with unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Compare- Smaller Unknown: More, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Carlos has 13 more comic
books than his friend David. Carlos has 30 comic books. How many comic books does David
have? Write an equation that represents this problem. Use a symbol for the unknown
number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 43 comic books
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 30 + 13 = *; 13 + * = 30).
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
33
OA Task 3b Name ____________________________________
2.OA.1, 2.NBT.5, 2.NBT.9
Compare- Smaller Unknown: More, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Carlos has 13 more comic books than his friend David. Carlos has 30 comic
books. How many comic books does David have?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ comic books
34
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 3c
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and comparing,
with unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Compare- Smaller Unknown: More, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Kevin has 23 more shiny
rocks than his friend Matthew. Kevin has 27 shiny rocks. How many shiny rocks does
Matthew have?
Write an equation that represents this problem. Use a symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 4 shiny rocks
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 27 - 23 = *; 23 + * = 27).
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
35
OA Task 3c Name ____________________________________
2.OA.1, 2.NBT.5, 2.NBT.9
Compare- Smaller Unknown: More, One-step
Formative Instructional and Assessment Tasks Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Kevin has 23 more shiny rocks than his friend Matthew. Kevin has 27 shiny
rocks. How many shiny rocks does Matthew have?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ shiny rocks
36
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 3d
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and comparing,
with unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Compare- Smaller Unknown: More, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Makayla has 22 more
mini mystery books than her sister Brittany. Makayla has 40 mini mystery books. How many
mini mystery books does Brittany have? Write an equation that represents this problem. Use
a symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 62 mini mystery books
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 22 + * = 40; 40 - 22 = *)
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
37
OA Task 3d Name ____________________________________
2.OA.1, 2.NBT.5, 2.NBT.9
Compare- Smaller Unknown: More, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Makayla has 22 more mini mystery books than her sister Brittany. Makayla
has 40 mini mystery books. How many mini mystery books does Brittany
have?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ mini mystery books
38
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 4a
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and comparing,
with unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Compare- Bigger Unknown: Fewer, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Luke has 5 fewer books
than Josh. Luke has 7 books. How many books does Josh have? Write an equation that
represents this problem. Use a symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 2 books
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., * - 5 = 7; 5 + 7 = *)
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
39
OA Task 4a Name ____________________________________
2.OA.1 , 2.NBT.5, 2.NBT.9
Compare- Bigger Unknown: Fewer, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Luke has 5 fewer books than Josh. Luke has 7 books. How many books does
Josh have?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ books
40
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 4b
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and comparing,
with unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Compare- Bigger Unknown: Fewer, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: The 2nd grade class has 9
fewer students than the 3rd grade class. The 2nd grade class has 22 students. How many
students are in the 3rd grade class? Write an equation that represents this problem. Use a
symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 31 students
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 9 + 22 = *)
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
41
OA Task 4b Name ____________________________________
2.OA.1 , 2.NBT.5, 2.NBT.9
Compare- Bigger Unknown: Fewer, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
The 2nd grade class has 9 fewer students than the 3rd grade class. The 2nd
grade class has 22 students. How many students are in the 3rd grade class?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ students
42
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 4c
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and comparing,
with unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Compare- Bigger Unknown: Fewer, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: There are 36 fewer apples
in the box than apples on the ground. There are 50 apples in the box. How many apples are
on the ground? Write an equation that represents this problem. Use a symbol for the
unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 86 apples
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 36 + 50 = *)
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
43
OA Task 4c Name ____________________________________
2.OA.1 , 2.NBT.5, 2.NBT.9
Compare- Bigger Unknown: Fewer, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
There are 36 fewer apples in the box than apples on the ground. There are 50
apples in the box. How many apples are on the ground?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ apples
44
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 4d
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and comparing,
with unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Compare- Bigger Unknown: Fewer, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: There are 11 fewer
cinnamon candies than chocolate candies. There are 30 cinnamon candies. How many
chocolate candies are there? Write an equation that represents this problem. Use a symbol
for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 41 chocolate candies
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 30 + 11 = *; 11 = * - 30)
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
45
OA Task 4d Name ____________________________________
2.OA.1 , 2.NBT.5, 2.NBT.9
Compare- Bigger Unknown: Fewer, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
There are 11 fewer cinnamon candies than chocolate candies. There are 30
cinnamon candies. How many chocolate candies are there?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ chocolate candies
46
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 5a
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and comparing,
with unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Add To-Result Unknown, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: John collected 67
baseball cards. His friend gave him 28 more baseball cards. How many cards does John
have now? Write an equation that represents this problem. Use a symbol for the unknown
number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 95 baseball cards
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 67 + 28 = *).
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
47
OA Task 5a Name ____________________________________
2.OA.1 , 2.NBT.5, 2.NBT.9
Add To-Result Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
John collected 67 baseball cards. His friend gave him 28 more baseball cards.
How many cards does John have now?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ baseball cards
48
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 5b
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and
comparing, with unknowns in all positions, e.g., by using drawings and equations with a
symbol for the unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Add To-Result Unknown, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Val has 26 butterflies for
the Science Fair. Sam brought 38 more butterflies for the Science Fair. How many
butterflies did they take to the science fair? Write an equation that represents this problem.
Use a symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 64 butterflies
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 26 + 38 = *).
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
49
OA Task 5b Name ____________________________________
2.OA.1 , 2.NBT.5, 2.NBT.9
Add To-Result Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Val has 26 butterflies for the Science Fair. Sam brought 38 more butterflies for
the Science Fair. How many butterflies did they take to the science fair?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ butterflies
50
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 5c
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and
comparing, with unknowns in all positions, e.g., by using drawings and equations with a
symbol for the unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Add To- Result Unknown, Two-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Ana brought 6 DVDs to a
party. Mark brought 7 DVDs to the party. Steve brought 8 DVDs to the party. How many
DVDs do they have for the party? Write an equation that represents this problem. Use a
symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 21 DVDs
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 6 + 7 + 8 = *)
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
51
OA Task 5c Name ____________________________________
2.OA.1 , 2.NBT.5, 2.NBT.9
Add To-Result Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Ana brought 6 DVDs to a party. Mark brought 7 DVDs to the party. Steve
brought 8 DVDs to the party. How many DVDs do they have for the party?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ DVDs
52
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 5d
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and comparing,
with unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Add To -Result Unknown, Two-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Benjamin has 7 baseball
cards. Kyle gave Benjamin 8 baseball cards. Jim gave Benjamin 3 more baseball cards.
How many cards does Benjamin have now? Write an equation that represents this problem.
Use a symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 18 baseball cards
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 7 + 8 + 3 = *)
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
53
OA Task 5d Name ____________________________________
2.OA.1 , 2.NBT.5, 2.NBT.9
Add To-Result Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Benjamin has 7 baseball cards. Kyle gave Benjamin 8 baseball cards. Jim gave
Benjamin 3 more baseball cards. How many cards does Benjamin have now?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ cards
54
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 6a
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and comparing,
with unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Add To: Change Unknown, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Lucas had 67 baseball
cards. His friend gave Lucas some more baseball cards. Now Lucas has 95 baseball cards.
How many baseball cards did his friend give Lucas? Write an equation that represents this
problem. Use a symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 28 baseball cards
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 67 + * = 95)
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
55
OA Task 6a Name ____________________________________
2.OA.1 , 2.NBT.5, 2.NBT.9
Add To: Change Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Lucas had 67 baseball cards. His friend gave Lucas some more baseball cards.
Now Lucas has 95 baseball cards. How many baseball cards did his friend give
Lucas?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ baseball cards
56
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 6b
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and comparing,
with unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Add To: Change Unknown, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Jalen had 30 marbles.
When he cleaned out his closet he found some more marbles. Now Jalen has 58 marbles.
How many marbles did Jalen find? Write an equation that represents this problem. Use a
symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 28 marbles
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 30 + * = 58; 58 – 30 = *)
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
57
OA Task 6b Name ____________________________________
2.OA.1 , 2.NBT.5, 2.NBT.9
Add To: Change Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Jalen had 30 marbles. When he cleaned out his closet he found some more
marbles. Now Jalen has 58 marbles. How many marbles did Jalen find?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ marbles
58
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 6c
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and
comparing, with unknowns in all positions, e.g., by using drawings and equations with a
symbol for the unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9. Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Add To: Change Unknown, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Pam has 17 cards of
animals from Africa. She has some cards from other continents. All together she has 90
cards. How many cards are from other continents? Write an equation that represents this
problem. Use a symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 73 cards
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., * = 90 – 17; 90 = * + 17)
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
59
OA Task 6c Name ____________________________________
2.OA.1 , 2.NBT.5, 2.NBT.9
Add To: Change Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Pam has 17 cards of animals from Africa. She has some cards from other
continents. All together she has 90 cards. How many cards are from other
continents?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ cards
60
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 7a
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one-and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and
comparing, with unknowns in all positions, e.g. by using drawings and equations with a
symbol for the unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9. Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Take From-Result Unknown, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: 60 apples were on the
shelf. 23 apples were sold. How many apples are on the shelf now? Write an equation that
represents this problem. Use a symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Basic Facts
 Creates easier or
known sums
 Doubles
 Other:
Complete
Understanding
• Correctly solves the problem: 37 apples
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 60 – 23 = *; 23 + * = 60)
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
61
OA Task 7a Name ____________________________________
2.OA.1 , 2.NBT.5, 2.NBT.9
Take From-Result Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
60 apples were on the shelf. 23 apples were sold. How many apples are on the
shelf now?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ apples
62
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 7b
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and comparing,
with unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9. Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Take From- Result Unknown, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Mrs. Hope’s class saw 76
butterflies in the garden. Some of the butterflies flew away. Now there are 49 butterflies in
the garden. How many butterflies flew away? Write an equation that represents this
problem. Use a symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 27 butterflies
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 76 – 49 = *; 76 = 49 + *).
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
63
OA Task 7b Name ____________________________________
2.OA.1 , 2.NBT.5, 2.NBT.9
Take From-Result Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Mrs. Hope’s class saw 76 butterflies in the garden. Some of the butterflies flew
away. Now there are 49 butterflies in the garden. How many butterflies flew
away?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ butterflies
64
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 7c
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one-and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and
comparing, with unknowns in all positions, e.g. by using drawings and equations with a
symbol for the unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9. Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Take From-Result Unknown, Two-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Avi drew 5 pictures to
enter in the school art contest. Erick drew 7 pictures. Avi spilled water on 2 of his pictures
and ruined them. How many pictures will Avi and Erick enter in the contest? Solve the
problem and use words, numbers or pictures to explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 10 pictures
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
65
OA Task 7c Name ____________________________________
2.OA.1 , 2.NBT.5, 2.NBT.9
Take From-Result Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Avi drew 5 pictures to enter in the school art contest. Erick drew 7 pictures.
Avi spilled water on 2 of his pictures and ruined them. How many pictures will
Avi and Erick enter in the contest?
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ pictures
66
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 8a
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one-and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and
comparing, with unknowns in all positions, e.g. by using drawings and equations with a
symbol for the unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9. Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Take From- Change Unknown, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: The principal had 38
balloons. Some balloons popped. Then the principal had 19 balloons. How many balloons
popped? Write an equation that represents this problem. Use a symbol for the unknown
number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 19 balloons
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 38 - * = 19; 19 + * = 38)
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
67
OA Task 8a Name ____________________________________
2.OA.1 1.NBT.5, 1.NBT.9
Take From- Change Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
The principal had 38 balloons. Some balloons popped. Then the principal had
19 balloons. How many balloons popped?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ balloons
68
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 8b
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one-and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and
comparing, with unknowns in all positions, e.g. by using drawings and equations with a
symbol for the unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9. Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Take From- Change Unknown, Two-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: 12 children were on the
baseball field. Some children left the baseball field to play on the swings. Then 2 more
children came to the baseball field. Now there are 8 children on the baseball field. How
many children left to play on the swings? Solve the problem and use words, numbers or
pictures to explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 6 children left the baseball
field
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
69
OA Task 8b Name ____________________________________
2.OA.1 1.NBT.5, 1.NBT.9
Take From- Change Unknown, Two-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
12 children were on the baseball field. Some children left the baseball field to play
on the swings. Then 2 more children came to the baseball field. Now there are
8 children on the baseball field. How many children left to play on the swings?
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ children
70
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 8c
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one-and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and
comparing, with unknowns in all positions, e.g. by using drawings and equations with a
symbol for the unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between ad

GRADE
2
PUBLIC SCHOOLS OF NORTH CAROLINA
State Board of Education | Department of Public Instruction
Formative Instructional & Assessment Tasks
for the Common Core State Standards in Mathematics
Word Document versions of the documents
http://commoncoretasks.wikispaces.com/
STATE BOARD OF EDUCATION
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from high school, globally competitive for work and postsecondary education and prepared for life in the 21st Century.
NC DEPARTMENT OF PUBLIC INSTRUCTION
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301 N. Wilmington Street :: Raleigh, North Carolina 27601-2825
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Rose Hill
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High Point
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Charlotte
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MELISSA E. BARTLETT
Roxboro
PATRICIA N. WILLOUGHBY
Raleigh
M0910
Table
of
Contents
1. Common
Core
State
Standards
........................................................................................................................................
1
2. Administration
Manual
.......................................................................................................................................................
3
3. Operations
&
Algebraic
Thinking
................................................................................................................................
15
4. Number
and
Operations
in
Base
Ten
........................................................................................................................
126
5. Measurement
and
Data
..................................................................................................................................................
158
6. Geometry
..............................................................................................................................................................................
203
7. Student
Record
Keeping
Forms
.................................................................................................................................
221
NOTE:
The
separate
Word
document
versions
of
each
section
can
be
found
online
at
http://commoncoretasks.wikispaces.com/
.
Common Core
State Standards
Operations and Algebraic Thinking
Represent and solve problems involving addition and subtraction.
2.OA.1 Use addition and subtraction within 100 to solve one- and two-step
word problems involving situations of adding to, taking from, putting
together, taking apart, and comparing, with unknowns in all positions,
e.g., by using drawings and equations with a symbol for the unknown
number to represent the problem. (Note: See Glossary, Table 1.)
Add and subtract within 20.
2.OA.2 Fluently add and subtract within 20 using mental strategies. (Note:
See standard 1.OA.6 for a list of mental strategies). By end of
Grade 2, know from memory all sums of two one-digit numbers.
Work with equal groups of objects to gain foundations for multiplication.
2.OA.3 Determine whether a group of objects (up to 20) has an odd or even
number of members, e.g., by pairing objects or counting them by 2s; write
an equation to express an even number as a sum of two equal addends.
2.OA.4 Use addition to find the total number of objects arranged in
rectangular arrays with up to 5 rows and up to 5 columns; write an
equation to express the total as a sum of equal addends.
Number and Operations in Base Ten
Understand place value.
2.NBT.1 Understand that the three digits of a three-digit number represent
amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0
tens, and 6 ones. Understand the following as special cases:
a. 100 can be thought of as a bundle of ten tens – called a “hundred.”
b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one,
two, three, four, five, six, seven, eight, or nine hundreds
(and 0 tens and 0 ones).
2.NBT.2 Count within 1000; skip-count by 5s, 10s, and 100s.
2.NBT.3 Read and write numbers to 1000 using base-ten numerals, number
names, and expanded form.
2.NBT.4 Compare two three-digit numbers based on meanings of the
hundreds, tens, and ones digits, using >, =, and < symbols to record
the results of comparisons.
Use place value understanding and properties of operations to add and
subtract.
2.NBT.5 Fluently add and subtract within 100 using strategies based on
place value, properties of operations, and/or the relationship
between addition and subtraction.
2.NBT.6 Add up to four two-digit numbers using strategies based on place
value and properties of operations.
2.NBT.7 Add and subtract within 1000, using concrete models or drawings
and strategies based on place value, properties of operations,
and/or the relationship between addition and subtraction; relate
the strategy to a written method. Understand that in adding or
subtracting three-digit numbers, one adds or subtracts hundreds
and hundreds, tens and tens, ones and ones; and sometimes it is
necessary to compose or decompose tens or hundreds.
2.NBT.8 Mentally add 10 or 100 to a given number 100-900, and mentally
subtract 10 or 100 from a given number 100-900.
2.NBT.9 Explain why addition and subtraction strategies work, using place
value and the properties of operations. (Note: Explanations may be
supported by drawings or objects.)
Measurement and Data
Measure and estimate lengths in standard units.
2.MD.1 Measure the length of an object by selecting and using appropriate
tools such as rulers, yardsticks, meter sticks, and measuring tapes.
2.MD.2 Measure the length of an object twice, using length units of
different lengths for the two measurements; describe how the two
measurements relate to the size of the unit chosen.
2.MD.3 Estimate lengths using units of inches, feet, centimeters, and meters.
2.MD.4 Measure to determine how much longer one object is than another,
expressing the length difference in terms of a standard length unit.
Relate addition and subtraction to length.
2.MD.5 Use addition and subtraction within 100 to solve word problems
involving lengths that are given in the same units, e.g., by using
drawings (such as drawings of rulers) and equations with a symbol
for the unknown number to represent the problem.
2.MD.6 Represent whole numbers as lengths from 0 on a number line
diagram with equally spaced points corresponding to the numbers
0, 1, 2, ..., and represent whole-number sums and differences within
100 on a number line diagram.
Second Grade – Standards
1. Extending understanding of base-ten notation – Students extend their
understanding of the base-ten system. This includes ideas of counting
in fives, tens, and multiples of hundreds, tens, and ones, as well as
number relationships involving these units, including comparing. Students
understand multi-digit numbers (up to 1000) written in base-ten notation,
recognizing that the digits in each place represent amounts of thousands,
hundreds, tens, or ones (e.g., 853 is 8 hundreds + 5 tens + 3 ones).
2. Building fluency with addition and subtraction – Students use
their understanding of addition to develop fluency with addition and
subtraction within 100. They solve problems within 1000 by applying their
understanding of models for addition and subtraction, and they develop,
discuss, and use efficient, accurate, and generalizable methods to
compute sums and differences of whole numbers in base-ten notation,
using their understanding of place value and the properties of operations.
They select and accurately apply methods that are appropriate for
the context and the numbers involved to mentally calculate sums and
differences for numbers with only tens or only hundreds.
3. Using standard units of measure – Students recognize the need for
standard units of measure (centimeter and inch) and they use rulers and
other measurement tools with the understanding that linear measure
involves iteration of units. They recognize that the smaller the unit, the
more iterations they need to cover a given length.
4. Describing and analyzing shapes – Students describe and analyze
shapes by examining their sides and angles. Students investigate,
describe, and reason about decomposing and combining shapes to make
other shapes. Through building, drawing, and analyzing two- and three-dimensional
shapes, students develop a foundation for understanding
attributes of two- and three-dimensional shapes, students develop a
foundation for understanding area, volume, congruence, similarity, and
symmetry in later grades.
Mathematical Practices
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
1
Work with time and money.
2.MD.7 Tell and write time from analog and digital clocks to the nearest five
minutes, using a.m. and p.m.
2.MD.8 Solve word problems involving dollar bills, quarters, dimes, nickels,
and pennies, using $ and ¢ symbols appropriately. Example: If you
have 2 dimes and 3 pennies, how many cents do you have?
Represent and interpret data.
2.MD.9 Generate measurement data by measuring lengths of several
objects to the nearest whole unit, or by making repeated
measurements of the same object. Show the measurements by
making a line plot, where the horizontal scale is marked off in whole-number
units.
2.MD.10 Draw a picture graph and a bar graph (with single-unit scale) to
represent a data set with up to four categories. Solve simple put
together, take-apart, and compare problems using information
presented in a bar graph. (Note: See Glossary, Table 1.)
Geometry
Reason with shapes and their attributes.
2.G.1 Recognize and draw shapes having specified attributes, such as
a given number of angles or a given number of equal faces. (Note:
Sizes are compared directly or visually, not compared by measuring.)
Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
2.G.2 Partition a rectangle into rows and columns of same-size squares and
count to find the total number of them.
2.G.3 Partition circles and rectangles into two, three, or four equal shares,
describe the shares using the words halves, thirds, half of, a third of,
etc., and describe the whole as two halves, three thirds, four fourths.
Recognize that equal shares of identical wholes need not have the
same shape.
2
Administration
Manual
K-2 Assessment in North Carolina
In response to North Carolina legislative and State Board requirements, the NC Department of
Public Instruction provides Local Education Agencies with state-developed assessments to be
implemented for Kindergarten, First and Second Grades. These assessments are to include
documented, on-going individualized assessments throughout the year and a summative
evaluation at the end of the year. These assessments monitor proficiency of the standards in the
North Carolina Standard Course of Study: Common Core State Standards for Mathematics.
Assessments may take the form of these state developed materials, adaptations of these
materials, or unique assessments adopted by local school boards. The intended purposes of these
assessments are:
• To provide information about progress of each student for instructional adaptations and early
interventions.
• To provide next-year teachers with information about the status of each of their incoming
students.
• To inform parents about the status of their children relative to grade-level standards at the
end of the year
• To provide the school and school district information about the achievement status and
progress of groups of students in grades K, 1, and 2.
The North Carolina Department of Public Instruction is committed to continued development of
quality teaching and on-going classroom assessment as essential preparation for the students to
master rigorous standards as defined by the NC Standard Course of Study: Common Core State
Standards and Essential Standards. We believe the strategies that engage students in self-assessment,
greater ownership of their learning, communicating, reasoning, problem posing and
problem solving result in long-term growth and learning.
Therefore, the Formative Instructional and Assessment Tasks for Mathematics are designed to
clarify the bond that links quality assessment and effective teaching- and subsequently effective
schools. Learning takes place one student at a time, and quality teaching and assessment is
essential in ensuring that every public school student will graduate from high school, globally
competitive for work and postsecondary education and prepared for life in the 21st Century.
These state-developed assessment materials are aligned with the Common Core State
Standards for Mathematics and may be adopted or modified as appropriate for individual
school districts. As you use them with students, add to and adapt the materials in order to
make them useful for each school’s unique situation. The North Carolina Department of
Public Instruction appreciates any suggestions and feedback, which will help improve upon
this resource. Feedback may be sent to NCDPI Elementary Mathematics Consultant Amy
Scrinzi (Amy.Scrinzi@dpi.nc.gov).
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K-2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION
The Purpose of the Formative Instructional and Assessment Tasks
The Formative Instructional and Assessment Tasks are provided as tools to use to assess
Kindergarten, First Grade and Second Grade students’ mathematical understanding as specified
in the NC Standard Course of Study: Common Core State Standards for Mathematics (CCSS-M).
Mathematical Concepts Assessed
The Formative Instructional and Assessment Tasks are designed to reveal the extent to which a
student knows and understands specific concepts. Moving beyond only whether an answer is
right or wrong, the tasks focus attention on the thinking and processes that all students use in
solving the tasks, with opportunities to demonstrate his or her knowledge, skill, and
understanding.
Therefore, the tasks assess the Common Core State Standards and highlight Standards for
Mathematical Practice that may emerge as students explore the tasks. The Continuum for
Understanding specifically addresses the conceptual understandings indicated in the CCSS-M.
The Standards for Mathematical Practice that are likely to emerge are indicated in bold for
each task.
Types of Tasks
When assessing young children, it is important to remember that
they frequently know more than they can record in traditional,
symbolic formats. “Age, fluency with language, and experiences
influence how successful students are likely to write a strong
explanation or offer an explanation orally” (Joyner & Muri, 2011).
Therefore interviews, as well as written responses, are provided.
Interview: The teacher asks a series of questions to one
student and carefully listens to the student’s responses
and observes the student’s strategies and thinking as the
student works.
Written Response: The teacher presents a problem to one or more students and asks the
students to use pictures, numbers, and words to show their thinking and explain their reasoning.
Since both correct answers and appropriate processes are valued in mathematics, teachers find that
observing students and talking with them are ways to provide students with opportunities to
demonstrate what they know and can apply in new situations. Thus, the teacher is encouraged to ask
the student clarifying questions during the assessment or after the assessment to gain a more
accurate picture of what the student knows and understands. Insight into children’s thinking helps
teachers build on what students understand, not just what they can do by memorizing processes.
“Without the
conversations or
written explanations,
we have no clue as
to the students’
logic behind their
wrong answers.”
(Joyner & Muri, 2011, p. 250)
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K-2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION
The Role of the Classroom Teacher
The classroom teacher uses the tasks in a formative manner. As defined by North Carolina
Department of Public Instruction, formative assessment is a
process
used
by
teachers
and
students
during
instruction
that
provides
feedback
to
adjust
ongoing
teaching
and
learning
to
help
students
improve
their
achievement
of
intended
instructional
outcomes. Therefore,
a teacher may use these tasks to:
• Determine prior knowledge regarding a concept that is about to be taught.
• Assess understanding throughout an instructional sequence to gain an understanding
of how to best meet the needs of all of the students in an on-going basis.
• Determine if the student is Developing Understanding of a particular concept or if the
student has Complete Understanding, demonstrating proficiency.
• Assess understanding after the instructional sequence to determine if all students are
proficient with that concept and are ready to move forward.
The teacher may administer the tasks to a whole class, small group of children, or an individual
student, depending on the purpose for collecting data. For example, the teacher may decide that
s/he would like to gain awareness of the entire class’ understanding of a particular concept.
Thus, the task(s) selected would then be administered to all of the students in the class. Other
times the teacher may need to determine what a particular student, or small group of students,
understands in order to plan the most effective mathematical experiences. Thus, the task(s)
selected would then be used with the selected student(s). Therefore, the assessment tasks can be
used in multiple ways with the purpose of informing instructional planning and practice.
The Role of the Local Education Agency (LEA)
A school district may decide to use the assessment tasks to create benchmark assessments,
aligning a collection of tasks to their unique pacing guide to be administered district-wide at
several points throughout the year. The classroom teacher scores the quarterly benchmark
assessments, sees students’ answers, observes misconceptions, and uses the data gathered to
inform further instruction and plan interventions or enrichments as needed (Joyner & Muri,
2011). The district uses the data from the benchmark assessments to gain a global view of how
students are performing within particular domains or clusters, determine which additional
instructional materials and resources may be needed, and discern particular topics and concepts
that teachers may need additional support or growth and work with principals and teachers to
plan professional development and coaching opportunities accordingly.
These state-developed assessment tasks are aligned with the North Carolina Standard
Course of Study: Common Core State Standards for Mathematics and may be adopted or
modified as appropriate for individual school districts. As they are used with students,
please add to and adapt the materials in order to make them useful for each school’s
unique situation. The North Carolina Department of Public Instruction appreciates any
suggestions and feedback, which will help improve upon this resource.
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K-2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION
The Components of the Formative Instructional & Assessment Tasks
The Formative Instructional and Assessment Tasks are composed of four parts:
1. Assessment Tasks
2. Student Forms
3. Blackline Masters
4. Class/Student Summaries
1. Assessment Tasks
The assessment tasks inform the classroom teacher of a) the Mathematical Concepts addressed,
b) the materials needed, c) the assessment task directions, the d) Continuum of Understanding,
and the e) Standards for Mathematical Practice.
a.) Mathematical Concepts: Designate the domain, cluster, and standard assessed. There may
be some tasks that assess multiple concepts.
Domain: Large group of related standards. Include: Counting and Cardinality (K),
Operations and Algebraic Thinking, Number and Operations in Base Ten, Measurement
and Data, and Geometry.
Cluster: Groups of related standards.
Standard: Define what students should understand and be able to do.
b.) Materials: Student and teacher materials needed to complete the task. Materials may
include: Blackline Master (BLM), Student Form (SF) or classroom materials. Provide additional
materials or substitute materials with those that students use during regular mathematics lessons
as needed.
c.) Task: Directions for the administering the task. May include “Teacher Talk”: dialogue for
the teacher to say to the student(s) while administering the task. Indicated in italics.
d.) Continuum of Understanding: Designates indicators: specific behaviors and skills that
signify if the student is Developing Understanding or demonstrates Complete Understanding.
Indicators: Specific behavior or skill within the continuum noted by a bullet.
Developing Understanding: If the student exhibits one OR more of the indicators listed,
then the student’s understanding is still evolving.
Complete Understanding: If the student exhibits ALL of the indicators listed, then the
student has demonstrated proficiency with that particular skills or concept on that one
particular task. Other tasks may be needed in order to confirm proficiency in that overall
skill or concept.
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K-2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION
In addition, there may be specific behaviors, strategies, concepts, or skills for which the teacher
is to observe. These are located to the right of the indicators. Answers to the tasks are also
provided in this area.
e.) Standards for Mathematical Practice: Describe processes and dispositions that
mathematically proficient students exhibit. Practices that are likely to emerge as a result of
completing the task are noted in BOLD. The teacher is encouraged to note which practices were
observed during the tasks as well as during daily instruction to gain a global picture of the
mathematical processes and dispositions that the student exhibits.
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K-2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION
The Formative Instructional and Assessment Tasks are composed of three additional parts:
1. Assessment Tasks
2. Student Forms
3. Blackline Masters
4. Class/Student Summaries
2. Student Forms
Student forms are provided as an option to use for all tasks that require a written response from
the student. These forms are located with the appropriate task and are designated as “SF”.
Teachers may copy, edit, or revise the forms as needed.
3. Blackline Masters
If a task requires a particular illustration or specific materials, then a blackline master is
included. These forms are located with the appropriate task and are designated as “BLM”.
Teachers may copy, edit, or revise forms as needed.
4. Class/Student Summaries
Class and Student Summaries are provided to help the classroom teacher collect and organize
data. These forms are located with the appropriate Domain/Cluster. These forms are provided as
Word documents allowing the teacher to type information as desired, change the size of the
space provided, or add additional columns or categories as needed. Teachers may copy, edit, or
revise the forms as needed.
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K-2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION
Selecting an Assessment Task
The Formative Instructional and Assessment Tasks are placed with the corresponding
Domain(s), Cluster(s), and Standard(s) on the common core assessment wiki. When searching
for a task, simply click on the domain and cluster of interest. Tasks will be located with each
standard assessed. In addition, each grade is provided with a comprehensive list of assessment
tasks and the standards to which they align.
NOTE: Some tasks assess multiple standards. Therefore, tasks are placed with the
primary standard assessed and additional standards assessed are noted in the table and
with the task directions.
When selecting a task, consider the following:
1. Designate a learning target. What skill or concept do you want students to know?
2. Identify the student(s). Are you curious about all of the students, a handful of students,
or one student in particular? Thinking about the student(s), what are you most interested
in learning that is related to the learning target?
3. Review and select the tasks. Locate tasks that are aligned with the learning target and
address your questions about the student(s).
4. Read the tasks carefully. Which tasks would best uncover student understanding for the
particular learning target? Does it need to be a new task or one previously administered?
Depending on the task and the learning target, the same task could be administered
multiple times over the course of the year.
5. Decide on an amount of tasks. To gain a more accurate view of student knowledge, one
task may not be enough. Perhaps one task, along with classroom evidence, will provide
an appropriate picture of the student’s understanding. Perhaps more than one task is
needed.
6. Decide how the tasks and materials will be presented. Will all students be assessed on
a task at the same time? If so, what will students who finish earlier/later than others do as
other students work? Will students move from one station to another? If so, what will
they do if they have questions about the task? Will students need access to optional
materials? If so, how will they be provided?
“Knowing what is to be learned is the starting point for instructional
planning. This knowledge is also the starting point for determining
what is to be assessed and how it will be measured.”
(Joyner & Muri, 2011, p. 55)
9
K-2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION
Assessing Students
During classroom instruction, the teacher facilitates learning by providing rich tasks, asking
probing questions, observing students, and scaffolding learning as appropriate. However, during
classroom assessment, the classroom teacher wants to learn what a student knows and is able to
do without the support typically provided during instruction.
In order to help the classroom teacher gather the best information possible from the tasks, the
teacher’s role becomes that of an observer. Refraining from any coaching, prompting, or
targeted questioning, the teacher only reads the assessment task to the student as many times as
needed and encourages the student to solve the problem to the best of his/her ability. On
occasion, a word provided in the directions may not make sense to the student and an alternative
word is provided as determined by the teacher. However, the classroom teacher is very careful
not to provide additional information that could cover up what the student does or doesn’t
understand. The goal of assessment is to un-cover student thinking so that instruction can
best meet his/her needs.
As the classroom teacher carefully observes students at work, s/he is finding out as much as
possible about what students are thinking and how they go about working on tasks. The teacher
may take notes on student strategies and behaviors, ask clarifying questions, or restate the
problem as needed. For example, do students work with confidence on the task or are there some
aspects that seem more difficult? Which ones? Can you determine why and make notes for
adjustments next time this happens? Oftentimes, the observation provides the most information
about student thinking.
Because young children frequently know more than they can record in traditional, symbolic
formats, it is important for the teacher to gather as much information about student
understanding as students work on the various tasks. As the teacher circulates, s/he asks
additional questions to learn as much as possible about students’ thinking. For example, the
teacher might say, “Tell me more about the picture you have drawn.” or “Tell me what you are
doing with the counters.” or “Tell me more about your thinking.” The teacher makes notes about
students’ responses.
Consider using the following clarifying questions to help understand student thinking:
• Tell me more about that.
• Can you show me?
• Why do you say that?
• What else can you tell me?
• How do you know?
• Why do you think that happened?
• Do you think this will happen every time?
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K-2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION
The assessment tasks can be administered individually, in small groups, or as a whole class,
depending on the purpose for the assessment task. Oftentimes, if a task is presented in a whole
class setting, the task requires the student to provide a written response. In this situation, the
teacher is unable to observe all children carefully to learn about their thinking. Therefore, if the
teacher has questions about a student’s work, the teacher is encouraged to ask follow up
questions, clarifying what the student wrote and gaining better insight into the student’s thinking.
When administering a task, consider the following:
1. Prepare the materials. Gather the materials needed for the task. All Blackline masters
and Student Forms are located next to the task. Additional materials from the general
classroom supplies may be needed. Will you need enough for the entire class or just one
or a few students?
2. Read through the task directions. The language that the teacher is to use when
administering a task is provided in italics. This ‘teacher talk’ is provided to help the
classroom teacher ask questions and provide information without guiding thinking.
Comments and notes to the teacher are not in italics. These comments provide prompts
or reminders to the teacher as the task is administered.
3. Read the Continuum for Understanding indicators. Much of the administration of an
assessment task is spent carefully observing children as they work. Read over the
indicators to know what you are looking for as the students solve the problem.
4. Observe the students carefully. How are the students solving the problem? What are
they using? Are they counting everything over and over or are they counting on? Do
they know 10 more or 10 less fluently, or are they counting up or back to figure it out?
Keep a clipboard, tablet, or other documentation devices to take notes as students work.
Oftentimes, the observation provides the most information about student thinking.
5. What’s Next? After a student has completed a task, will s/he head back to Math
Stations? Move on to the next item on his/her contract? Get his/her snack and join the
others on the carpet or on the playground? Use the limited time you have wisely and
refrain from having students wait for one another by planning “what’s next”.
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K-2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION
Interpreting Data and Making Inferences
The primary purpose of an assessment is to discern student understanding and then use this
knowledge to plan instruction and teach students according to their needs. Because the tasks that
are provided are considered assessments rather than evaluations, proficiency scores are not
provided. Thus, an item is not simply marked as “correct” or “incorrect” or “proficient” or “not
proficient”. Instead, the Continuum of Understanding is provided to help inform the teacher
about the depth to which the student demonstrates understanding.
As student responses are reviewed, the teacher uses the Continuum of Understanding to
determine which strategies, skills, and understanding the student exhibits. Pay particular
attention to what the student DOES understand and what the student does NOT. Both are
equally important in determining the next instructional steps.
The overall goal is that by the end of the year, all students will have become proficient with the
mathematics described for their grade level. Proficient means that they can model and explain
the concepts, they can use the mathematics appropriately and accurately, and they are fluent and
comfortable in applying mathematics.
Giving meaning to students’ words and actions is
not a simple task, but it is critical that the
interpretations are as accurate as possible. Because
decisions about students and teaching arise from
the interpretations, teachers must think carefully
about the mathematics they are teaching, the
continuum of understandings and skills related to
the learning targets, and the information they have
learned from the assessment.
When interpreting data and making inferences, consider the following:
1. Ask Questions: If a student response is unclear or additional questions are needed to
gain clarification about student thinking, have a discussion with the student. Share the
work with the student and ask questions that will uncover the student’s thinking.
Remember, this is not a time to teach the student something s/he may have answered
incorrectly. This is a time to better understand the student’s thinking so that future
instruction can meet his/her needs.
2. Types of Mistakes: Look beyond whether an item’s answer was correct or incorrect by
looking carefully at the types of mistakes that were made. Some mistakes that children
make come from a lack of information. At other times mistakes reflect a lack of
understanding. Remember that there is logic behind students’ answers. The teacher must
look for the reasons for the responses, dig deep and identify any misconceptions that may
exist. Ask questions or seek clarification if needed. “Without the conversations or
written explanations, we have no clue as to the students’ logic behind their wrong
answers.” (Joyner & Muri, 2011, p. 250)
“Unless we take the time to
analyze incorrect responses,
we may have no clue as to why
students miss questions.”
(Joyner & Muri, 2011, p. 123)
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K-2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION
3. Note Strategies Used: The Continuum of Understanding provides strategies of
particular interest as well as additional skills and knowledge that the student may exhibit.
Carefully note how the student solves the problem present in the task. What strategies
does the student use? Does the student continually use a counting strategy rather than
moving forward to making tens? Are there strategies that are never used? What
strategies need to be highlighted during future instruction?
4. Organize Data: How will you capture the notes made about the student work? Will data
be recorded by individual student, on class summary sheets, or both? Some teachers may
wish to make notes on the task direction sheet for each student and staple it to the student
work. Other teachers may want to use the individual student recording form provided to
capture notes, using the task direction sheet to guide the structure of the notes. Teachers
may also want to compile class data on the class summary sheets to gain a global
perspective of the class as a whole, determine small groups, and determine next
instructional steps.
Assigning meaning to students’ words, actions, and products is perhaps the most difficult part of
assessment. However, teachers must deal with students’ misconceptions as well as their
strengths if students are going to be successful. If decisions are made from too little evidence or
misleading evidence teachers may not plan the necessary classroom experiences for the students
to refine their thinking.
Therefore, it is important to note that these assessment tasks will provide only a part of the
evidence of students’ knowledge and understanding and will be combined with other information
the teacher has gathered about the student. These assessments are not intended to provide a
complete picture of a student’s mathematics understandings. These assessments and additional
student products and anecdotal information will need to be combined to gain the most accurate
picture of student’s ability and understanding of mathematics.
References:
Joyner, J. & Muri, M. (2011). INFORMative assessment: Formative assessment to improve math achievement. Sausalito, CA: Math Solutions.
“When we do not have an opportunity to see the steps or
procedures that students use in determining answers or if students
do not explain their thinking, the correct answers may be the
results or informed guesses rather than solid understanding.”
(Joyner & Muri, 2011, p. 122)
13
K-2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION
A Special Thank-You
The development of the NC Department of Public Instruction K-2 Formative Instructional and
Assessment Tasks was a collaborative effort with a diverse group of dynamic teachers, coaches,
administrators, university faculty, and NCDPI staff. We are very appreciative of all of the time,
support, ideas, and suggestions made in an effort to provide North Carolina with quality
formative assessment items for Kindergarten, First, and Second Grade. The North Carolina
Department of Public Instruction appreciates any suggestions and feedback, which will help
improve upon this resource. Please send all correspondence to Barbara Bissell
(barbara.bissell@dpi.nc.gov) and Amy Scrinzi (amy.scrinzi@dpi.nc.gov).
K-2 Assessment Committee
The K-2 Assessment Committee led the work of the K-2 Assessments. With support of their
school and district, they volunteered their time and effort to develop the K-2 Formative
Instructional and Assessment Tasks.
Jill Burke, First Grade Teacher, Chapel Hill-Carrboro City Schools
Leanne Daughtry, District Office, Johnston County Schools
Andi Greene, First Grade Teacher, Edgecombe County Schools
Tery Gunter, Second Grade Teacher, Durham County Schools
Tesha Isler, Teaching/Learning Coach, Wayne County Schools
Patty Jordan, Second Grade Teacher, Wake County Schools
Rebecca Kidd, Kindergarten Teacher, Asheboro City Schools
Loryn Morrison, District Lead Teacher, Davidson County Schools
Becky Pearce, Kindergarten Teacher, Guilford County Schools
Kitty Rutherford, NCDPI Elementary Consultant
Amy Scrinzi, NCDPI Elementary Consultant
District Support
In a true collaborative effort, districts in North Carolina that had begun implementing the Common
Core State Standards during the 2011-2012 school year voluntarily shared their assessment efforts
with the K-2 Assessment Committee. Many of the final tasks presented are a direct result of this
collaborative support.
Cabarrus, Charlotte-Mecklenburg, Cleveland, Currituck, Davidson, Iredell-Statesville,
Kannapolis, and Union
Critical Friends
Our Critical Friends carefully reviewed the assessment tasks, offered specific feedback, and
provided suggestions for additional tasks as needed. Their feedback guided the final development
of the assessment tasks.
Melanie Burgess, Jeanette Cox, Donna Dalke, Ana Floyd, Sharon Frost, Royanna Jackson,
Jeane Joyner, Rendy King, Carol Midgett, Drew Polly, Wendy Rich, Karen Young, and
Pam Zelando
14
Operations &
Algebraic Thinking
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 1a
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and comparing,
with unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Add To-Start Unknown, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Daniel had some stickers.
His brother gave him 5 more stickers. Now Daniel has 18 stickers. How many stickers did
Daniel have to start with? Write an equation that represents this problem. Use a symbol for
the unknown number.
Solve the problem and use words, numbers or pictures to explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 13 stickers
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 18 - 5 = *; * + 5 = 18).
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
15
OA Task 1a Name ____________________________________
2.OA.1 Add To-Start Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Daniel had some stickers. His brother gave him 5 more stickers. Now Daniel
has 18 stickers. How many stickers did Daniel have to start with?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ stickers
16
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 1b
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and comparing,
with unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Add To-Start Unknown, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Jayden has some baseball
cards. His friend gave him 28 more baseball cards. Now Jayden has 95 baseball cards. How
many baseball cards did John start with? Write an equation that represents this problem.
Use a symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 67 baseball cards
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts
• Equation is accurate (e.g., 95 – 28 = *; 28 + * = 95).
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
17
OA Task 1b Name ____________________________________
2.OA.1 Add To-Start Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Jayden has some baseball cards. His friend gave him 28 more baseball cards.
Now Jayden has 95 baseball cards. How many baseball cards did Jayden start
with?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ baseball cards
18
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 1c
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and
comparing, with unknowns in all positions, e.g., by using drawings and equations with a
symbol for the unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Add To-Start Unknown, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Alice has some pennies.
Her dad gave her 48 more pennies. Now Alice has 83 pennies. How many pennies did Alice
start with? Write an equation that represents this problem. Use a symbol for the unknown
number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 35 pennies
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., * + 48 = 83; 83 – 48 = *).
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
19
OA Task 1c Name ____________________________________
2.OA.1 Add To-Start Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Alice has some pennies. Her dad gave her 48 more pennies. Now Alice has 83
pennies. How many pennies did Alice start with?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ pennies
20
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 1d
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and comparing,
with unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Add To-Start Unknown, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Nevaeh had some jewels.
She gave 11 jewels to her sister. Now Nevaeh has 79 jewels. How many jewels did Nevaeh
have to start with? Write an equation that represents this problem. Use a symbol for the
unknown number.
Solve the problem and use words, numbers or pictures to explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 90 jewels
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 48 - 11 = *; * + 11 = 48).
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
21
OA Task 1d Name ____________________________________
2.OA.1 Add To-Start Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Nevaeh had some jewels. She gave 11 jewels to her sister. Now Nevaeh has 79
jewels. How many jewels did Nevaeh have to start with?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ jewels
22
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 2a
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and comparing,
with unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Take From-Start Unknown, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Some baseball cards were
on the table. Sam took 42 baseball cards. Then there were 26 baseball cards on the table.
How many baseball cards were on the table before? Write an equation that represents this
problem. Use a symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 68 baseball cards
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., * - 42 = 26; 26 + 42 = *).
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
23
OA Task 2a Name ____________________________________
2.OA.1 Take From-Start Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Some baseball cards were on the table. Sam took 42 baseball cards. Then there
were 26 baseball cards on the table. How many baseball cards were on the
table before?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ baseball cards
24
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 2b
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and
comparing, with unknowns in all positions, e.g., by using drawings and equations with a
symbol for the unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Take From-Start Unknown, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Some players are on the
basketball court. 14 players left. Then there were 16 players on the basketball court. How
many players were on the basketball court before? Write an equation that represents this
problem. Use a symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 30 players
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., * - 14 = 16; 14 + 16 = *).
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
25
OA Task 2b Name ____________________________________
2.OA.1 Take From-Start Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Some players are on the basketball court. 14 players left. Then there were 16
players on the basketball court. How many players were on the basketball
court before?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ players
26
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 2c
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and
comparing, with unknowns in all positions, e.g., by using drawings and equations with a
symbol for the unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Take From-Start Unknown, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Some fish are swimming
in the stream. 23 fish swam away. Then there were 31 fish swimming in the stream. How
many fish were swimming in the stream before? Write an equation that represents this
problem. Use a symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 54 fish
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g. 23 + 31 = *).
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
27
OA Task 2c Name ____________________________________
2.OA.1 Take From-Start Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Some fish are swimming in the stream. 23 fish swam away. Then there were 31 fish
swimming in the stream. How many fish were swimming in the stream before?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ fish
28
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 2d
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and
comparing, with unknowns in all positions, e.g., by using drawings and equations with a
symbol for the unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Take From-Start Unknown, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: There were some Legos in
a bucket. 50 Legos spilled out of the bucket. Then there were 33 Legos in the bucket. How
many Legos were in the bucket before? Write an equation that represents this problem. Use
a symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 83 Legos
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 50 + 33 = *; * - 50 = 33).
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
29
OA Task 2d Name ____________________________________
2.OA.1 Take From-Start Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
There were some Legos in a bucket. 50 Legos spilled out of the bucket. Then
there were 33 Legos in the bucket. How many Legos were in the bucket
before?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ Legos
30
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 3a
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and comparing,
with unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Compare- Smaller Unknown: More, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Daniella has 9 more
bracelets than Katie. Katie has 22 bracelets. How many bracelets does Daniella have?
Write an equation that represents this problem. Use a symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 31 bracelets
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 9 + 22 = *).
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
31
OA Task 3a Name ____________________________________
2.OA.1 , 2.NBT.5, 2.NBT.9
Compare- Smaller Unknown: More, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Daniella has 9 more bracelets than Katie. Katie has 22 bracelets. How many
bracelets does Daniella have?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ bracelets
32
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 3b
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and comparing,
with unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Compare- Smaller Unknown: More, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Carlos has 13 more comic
books than his friend David. Carlos has 30 comic books. How many comic books does David
have? Write an equation that represents this problem. Use a symbol for the unknown
number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 43 comic books
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 30 + 13 = *; 13 + * = 30).
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
33
OA Task 3b Name ____________________________________
2.OA.1, 2.NBT.5, 2.NBT.9
Compare- Smaller Unknown: More, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Carlos has 13 more comic books than his friend David. Carlos has 30 comic
books. How many comic books does David have?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ comic books
34
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 3c
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and comparing,
with unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Compare- Smaller Unknown: More, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Kevin has 23 more shiny
rocks than his friend Matthew. Kevin has 27 shiny rocks. How many shiny rocks does
Matthew have?
Write an equation that represents this problem. Use a symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 4 shiny rocks
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 27 - 23 = *; 23 + * = 27).
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
35
OA Task 3c Name ____________________________________
2.OA.1, 2.NBT.5, 2.NBT.9
Compare- Smaller Unknown: More, One-step
Formative Instructional and Assessment Tasks Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Kevin has 23 more shiny rocks than his friend Matthew. Kevin has 27 shiny
rocks. How many shiny rocks does Matthew have?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ shiny rocks
36
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 3d
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and comparing,
with unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Compare- Smaller Unknown: More, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Makayla has 22 more
mini mystery books than her sister Brittany. Makayla has 40 mini mystery books. How many
mini mystery books does Brittany have? Write an equation that represents this problem. Use
a symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 62 mini mystery books
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 22 + * = 40; 40 - 22 = *)
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
37
OA Task 3d Name ____________________________________
2.OA.1, 2.NBT.5, 2.NBT.9
Compare- Smaller Unknown: More, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Makayla has 22 more mini mystery books than her sister Brittany. Makayla
has 40 mini mystery books. How many mini mystery books does Brittany
have?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ mini mystery books
38
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 4a
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and comparing,
with unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Compare- Bigger Unknown: Fewer, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Luke has 5 fewer books
than Josh. Luke has 7 books. How many books does Josh have? Write an equation that
represents this problem. Use a symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 2 books
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., * - 5 = 7; 5 + 7 = *)
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
39
OA Task 4a Name ____________________________________
2.OA.1 , 2.NBT.5, 2.NBT.9
Compare- Bigger Unknown: Fewer, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Luke has 5 fewer books than Josh. Luke has 7 books. How many books does
Josh have?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ books
40
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 4b
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and comparing,
with unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Compare- Bigger Unknown: Fewer, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: The 2nd grade class has 9
fewer students than the 3rd grade class. The 2nd grade class has 22 students. How many
students are in the 3rd grade class? Write an equation that represents this problem. Use a
symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 31 students
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 9 + 22 = *)
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
41
OA Task 4b Name ____________________________________
2.OA.1 , 2.NBT.5, 2.NBT.9
Compare- Bigger Unknown: Fewer, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
The 2nd grade class has 9 fewer students than the 3rd grade class. The 2nd
grade class has 22 students. How many students are in the 3rd grade class?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ students
42
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 4c
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and comparing,
with unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Compare- Bigger Unknown: Fewer, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: There are 36 fewer apples
in the box than apples on the ground. There are 50 apples in the box. How many apples are
on the ground? Write an equation that represents this problem. Use a symbol for the
unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 86 apples
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 36 + 50 = *)
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
43
OA Task 4c Name ____________________________________
2.OA.1 , 2.NBT.5, 2.NBT.9
Compare- Bigger Unknown: Fewer, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
There are 36 fewer apples in the box than apples on the ground. There are 50
apples in the box. How many apples are on the ground?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ apples
44
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 4d
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and comparing,
with unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Compare- Bigger Unknown: Fewer, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: There are 11 fewer
cinnamon candies than chocolate candies. There are 30 cinnamon candies. How many
chocolate candies are there? Write an equation that represents this problem. Use a symbol
for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 41 chocolate candies
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 30 + 11 = *; 11 = * - 30)
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
45
OA Task 4d Name ____________________________________
2.OA.1 , 2.NBT.5, 2.NBT.9
Compare- Bigger Unknown: Fewer, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
There are 11 fewer cinnamon candies than chocolate candies. There are 30
cinnamon candies. How many chocolate candies are there?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ chocolate candies
46
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 5a
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and comparing,
with unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Add To-Result Unknown, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: John collected 67
baseball cards. His friend gave him 28 more baseball cards. How many cards does John
have now? Write an equation that represents this problem. Use a symbol for the unknown
number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 95 baseball cards
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 67 + 28 = *).
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
47
OA Task 5a Name ____________________________________
2.OA.1 , 2.NBT.5, 2.NBT.9
Add To-Result Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
John collected 67 baseball cards. His friend gave him 28 more baseball cards.
How many cards does John have now?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ baseball cards
48
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 5b
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and
comparing, with unknowns in all positions, e.g., by using drawings and equations with a
symbol for the unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Add To-Result Unknown, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Val has 26 butterflies for
the Science Fair. Sam brought 38 more butterflies for the Science Fair. How many
butterflies did they take to the science fair? Write an equation that represents this problem.
Use a symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 64 butterflies
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 26 + 38 = *).
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
49
OA Task 5b Name ____________________________________
2.OA.1 , 2.NBT.5, 2.NBT.9
Add To-Result Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Val has 26 butterflies for the Science Fair. Sam brought 38 more butterflies for
the Science Fair. How many butterflies did they take to the science fair?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ butterflies
50
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 5c
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and
comparing, with unknowns in all positions, e.g., by using drawings and equations with a
symbol for the unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Add To- Result Unknown, Two-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Ana brought 6 DVDs to a
party. Mark brought 7 DVDs to the party. Steve brought 8 DVDs to the party. How many
DVDs do they have for the party? Write an equation that represents this problem. Use a
symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 21 DVDs
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 6 + 7 + 8 = *)
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
51
OA Task 5c Name ____________________________________
2.OA.1 , 2.NBT.5, 2.NBT.9
Add To-Result Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Ana brought 6 DVDs to a party. Mark brought 7 DVDs to the party. Steve
brought 8 DVDs to the party. How many DVDs do they have for the party?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ DVDs
52
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 5d
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and comparing,
with unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Add To -Result Unknown, Two-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Benjamin has 7 baseball
cards. Kyle gave Benjamin 8 baseball cards. Jim gave Benjamin 3 more baseball cards.
How many cards does Benjamin have now? Write an equation that represents this problem.
Use a symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 18 baseball cards
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 7 + 8 + 3 = *)
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
53
OA Task 5d Name ____________________________________
2.OA.1 , 2.NBT.5, 2.NBT.9
Add To-Result Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Benjamin has 7 baseball cards. Kyle gave Benjamin 8 baseball cards. Jim gave
Benjamin 3 more baseball cards. How many cards does Benjamin have now?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ cards
54
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 6a
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and comparing,
with unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Add To: Change Unknown, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Lucas had 67 baseball
cards. His friend gave Lucas some more baseball cards. Now Lucas has 95 baseball cards.
How many baseball cards did his friend give Lucas? Write an equation that represents this
problem. Use a symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 28 baseball cards
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 67 + * = 95)
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
55
OA Task 6a Name ____________________________________
2.OA.1 , 2.NBT.5, 2.NBT.9
Add To: Change Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Lucas had 67 baseball cards. His friend gave Lucas some more baseball cards.
Now Lucas has 95 baseball cards. How many baseball cards did his friend give
Lucas?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ baseball cards
56
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 6b
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and comparing,
with unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Add To: Change Unknown, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Jalen had 30 marbles.
When he cleaned out his closet he found some more marbles. Now Jalen has 58 marbles.
How many marbles did Jalen find? Write an equation that represents this problem. Use a
symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 28 marbles
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 30 + * = 58; 58 – 30 = *)
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
57
OA Task 6b Name ____________________________________
2.OA.1 , 2.NBT.5, 2.NBT.9
Add To: Change Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Jalen had 30 marbles. When he cleaned out his closet he found some more
marbles. Now Jalen has 58 marbles. How many marbles did Jalen find?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ marbles
58
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 6c
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and
comparing, with unknowns in all positions, e.g., by using drawings and equations with a
symbol for the unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9. Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Add To: Change Unknown, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Pam has 17 cards of
animals from Africa. She has some cards from other continents. All together she has 90
cards. How many cards are from other continents? Write an equation that represents this
problem. Use a symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 73 cards
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., * = 90 – 17; 90 = * + 17)
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
59
OA Task 6c Name ____________________________________
2.OA.1 , 2.NBT.5, 2.NBT.9
Add To: Change Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Pam has 17 cards of animals from Africa. She has some cards from other
continents. All together she has 90 cards. How many cards are from other
continents?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ cards
60
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 7a
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one-and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and
comparing, with unknowns in all positions, e.g. by using drawings and equations with a
symbol for the unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9. Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Take From-Result Unknown, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: 60 apples were on the
shelf. 23 apples were sold. How many apples are on the shelf now? Write an equation that
represents this problem. Use a symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Basic Facts
 Creates easier or
known sums
 Doubles
 Other:
Complete
Understanding
• Correctly solves the problem: 37 apples
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 60 – 23 = *; 23 + * = 60)
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
61
OA Task 7a Name ____________________________________
2.OA.1 , 2.NBT.5, 2.NBT.9
Take From-Result Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
60 apples were on the shelf. 23 apples were sold. How many apples are on the
shelf now?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ apples
62
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 7b
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and comparing,
with unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9. Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Take From- Result Unknown, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Mrs. Hope’s class saw 76
butterflies in the garden. Some of the butterflies flew away. Now there are 49 butterflies in
the garden. How many butterflies flew away? Write an equation that represents this
problem. Use a symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 27 butterflies
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 76 – 49 = *; 76 = 49 + *).
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
63
OA Task 7b Name ____________________________________
2.OA.1 , 2.NBT.5, 2.NBT.9
Take From-Result Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Mrs. Hope’s class saw 76 butterflies in the garden. Some of the butterflies flew
away. Now there are 49 butterflies in the garden. How many butterflies flew
away?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ butterflies
64
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 7c
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one-and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and
comparing, with unknowns in all positions, e.g. by using drawings and equations with a
symbol for the unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9. Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Take From-Result Unknown, Two-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: Avi drew 5 pictures to
enter in the school art contest. Erick drew 7 pictures. Avi spilled water on 2 of his pictures
and ruined them. How many pictures will Avi and Erick enter in the contest? Solve the
problem and use words, numbers or pictures to explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 10 pictures
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
65
OA Task 7c Name ____________________________________
2.OA.1 , 2.NBT.5, 2.NBT.9
Take From-Result Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Avi drew 5 pictures to enter in the school art contest. Erick drew 7 pictures.
Avi spilled water on 2 of his pictures and ruined them. How many pictures will
Avi and Erick enter in the contest?
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ pictures
66
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 8a
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one-and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and
comparing, with unknowns in all positions, e.g. by using drawings and equations with a
symbol for the unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9. Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Take From- Change Unknown, One-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: The principal had 38
balloons. Some balloons popped. Then the principal had 19 balloons. How many balloons
popped? Write an equation that represents this problem. Use a symbol for the unknown
number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to
explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Equation is inaccurate.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 19 balloons
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Equation is accurate (e.g., 38 - * = 19; 19 + * = 38)
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
67
OA Task 8a Name ____________________________________
2.OA.1 1.NBT.5, 1.NBT.9
Take From- Change Unknown, One-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
The principal had 38 balloons. Some balloons popped. Then the principal had
19 balloons. How many balloons popped?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ balloons
68
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 8b
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one-and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and
comparing, with unknowns in all positions, e.g. by using drawings and equations with a
symbol for the unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.9. Explain why addition and subtraction strategies work, using place value and the
properties of operations.
Take From- Change Unknown, Two-step
Materials SF, Pencil, Paper, counters and base ten materials available
Task Provide materials to the student. Read the problem to the student: 12 children were on the
baseball field. Some children left the baseball field to play on the swings. Then 2 more
children came to the baseball field. Now there are 8 children on the baseball field. How
many children left to play on the swings? Solve the problem and use words, numbers or
pictures to explain your reasoning.
Continuum of Understanding
Developing
Understanding
• Incorrectly solves the problem.
• Relies on counting as primary strategy for solving
problem.
• Explanation is lacking in detail or non-existent.
Strategy(ies) Used:
 Counting All
 Counting On
 Makes Tens
 Basic Facts
 Creates easier or
known sums
 Doubles
 Doubles +/- 1, 2
 Other:
Complete
Understanding
• Correctly solves the problem: 6 children left the baseball
field
• Successfully uses strategies such as making tens, creates
easier or known sums, and basic facts.
• Explanation is clear.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
69
OA Task 8b Name ____________________________________
2.OA.1 1.NBT.5, 1.NBT.9
Take From- Change Unknown, Two-step
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
12 children were on the baseball field. Some children left the baseball field to play
on the swings. Then 2 more children came to the baseball field. Now there are
8 children on the baseball field. How many children left to play on the swings?
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ children
70
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
OA Task 8c
Domain Operations and Algebraic Thinking
Number and Operations in Base Ten
Cluster Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one-and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and
comparing, with unknowns in all positions, e.g. by using drawings and equations with a
symbol for the unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between ad